Cosmology And String Theory

Monday, January 07, 2019

Cosmology And String Theory

Alexander Friedmann found the big bang solution to Einstein's general relativity equations which predicted that the universe started from a point of infinite compression and expanded. Hubble supported this as he saw that galaxies were rushing away from each other suggesting they started at a single point.

The Standard Model Of Cosmology

15 Billion years ago, the universe was a single point. (Note that the big bang occurred at your current location as well as everywhere else because all locations were the same location at the start). About a 100,000th of a second after the bang, the universe was cool enough for quarks to clump. For the next 3 minutes these quarks were able to combine to form hydrogen and helium nuclei. For the next 100,000 years the universe cooled until it was a few thousand kelvin. At this point electrons started moving slowly enough to attach to nuclei to form atoms.

About a billion years after that, it was cool enough to start forming galaxies, stars and planets etc...

The prediction of Cosmic Microwave Background Radiation (CMBR) provides strong evidence for the big bang and confirms the theory up to when photons could first move freely in the universe (a few 100,000 years after the big bang).
By using nuclear theory, it can be predicted that 23% of the universe should be helium and this is true as well. This improves our certainty on the theory of cosmology and we can say we are correct to a hundredth of a second after the big bang.

Past this moment however, general relativity and quantum field theory is needed together because of the high energy and mass in a very small area. This is where string theory may be able to provide some answers.

The Horizon Problem

Why is CMBR on opposite sides of the universe the same temperature?
This is the horizon problem and the standard model of cosmology fails to explain this.

For positions separated by large distances to be the same temperature, there had to have been a time when they were close and had time to transfer energy between themselves to reach equilibrium.
The big bang does predict they were close but when you think about time as well, you can see there was not enough time for them to transfer energy. It turns out that the uniform temperature of CMBR that we see does not support the standard model of cosmology.

The speed of light is the cosmic speed limit and so two regions of space may have been able to exchange heat if the distance between them was once less than the speed of light x the age of the universe.

In order to make the distance between two distant regions 186,000 miles, we have to go back in history to less than one second after the big bang and so they could not interact. If the distance was 100 miles, again we would have to go back in time so far that they would have had no time to interact. To get two regions of space close enough, we have to go back very far, so far that there is not enough time for an influence to travel between the two regions of space. The universe does not shrink fast enough.

This is because the pull of gravity is always slowing the rate of expansion. To half the separation between two points we have to go more than halfway back in time.

Alan Guth's solution to the general relativity equations solves the horizon problem however. It predicts that for a short period of time in the early universe, there was a period of very fast exponential expansion. This meant when halving the separation between two points, because inflation was increasing the rate of expansion, we can go less than halfway back in history. This gives two separated regions of space more time to exchange heat. This is the Inflationary Cosmological Model and it predicts from 10^-36s to 10^-34s after the big bang, the universe expanded by a factor of at least 10³⁰. After this, normal expansion predicted in the standard model of cosmology continued.

So now all that is left is to decide what happened in those moments before inflation. What happened from the big bang to the Planck time? Using general relativity, the prediction is that the universe just gets ever smaller, hotter and denser until when t = 0, we have a universe of infinite density.

String Theory

The first thing that string theory changes is that the universe can't shrink to below the Planck length because of the R - 1/R relationship.

The second change is that there may be 11 space-time dimensions and so we have to think about how all 11 changed in the early moments of the universe. As we go back in time, the temperature of the universe increases until it hits a maximum and then begins to decrease. At the beginning therefore, all spacial dimensions must have been the smallest possible size which is the Planck length.

We have 3 extended spacial dimensions so an obvious question is why 3? Strings are extended objects and so can wrap around dimensions that are curled and constrict growth.
If a string and an anti-string partner then come into contact, they annihilate giving an unwrapped string. If this happens in a certain way, the constriction around the dimension can be eliminated.
This can explain why we have 3 extended spacial dimensions. 2 point particles on a 1D line will definitely collide if they are not moving at the same velocity. But if you turn this into a 2D plane, the chances of collisions decreases massively.
This is the same with strings, if you have 3 or less circular spacial dimensions, strings are very likely to collide. This means in the early moments of the universe, all 10 spacial dimensions tried to expand. Annihilations then took place in 3 of them which reduced the constriction on them. This caused them to expand slightly. Once they had expanded, strings were less likely to wrap around them because it takes more energy for a string to wrap around a dimension as it increases in size. This means it made them even more likely to grow and we end up with the universe we see today,.

Calabi-Yau Spaces

In the early moments of the universe, the Calabi-Yau spaces in the universe would have been pretty crazy. It is likely that they went through a rapid cycles of tearing and reconnecting under going many flop-transitions and maybe some conifold transitions. As the universe cooled however, this slowed down and the shape settled into the one we have now with its corresponding physical characteristics. This means a way of deciding which Calabi-Yau space we have right now may come down to cosmology.

A Pre Big Bang Theory

Another version of the big bang with string theory by Veneziano and Gasperini is that instead of the universe starting with 10 Planck sized spacial dimensions, is that it was a very cold with nearly infinite spacial expanse. An instability then kicked in which caused each point in the universe to rush away quickly. This caused space-time to become increasing curved which increased temperature and energy density in these local regions. A tiny region within this expanse then looks like our universe that underwent cosmic inflation in its early moments.
This theory therefore has the solution to the horizon problem built into the theory.

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